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Showing papers on "Biorthogonal system published in 1977"


Journal ArticleDOI
TL;DR: In this paper, sufficient conditions are established for the convergence of the biorthogonal series solving edge problems which arise in elasticity and in Stokes flow in cavities, which are problems previously considered to be intractable to analysis.
Abstract: Sufficient conditions are established for the convergence of the biorthogonal series solving edge problems which arise in elasticity and in Stokes flow in cavities. These conditions and those given in Part I, (D. D. Joseph, The convergence of biorthogonal series for biharmonic and Stokes flow edge problems, SIAM, J. Appl. Math., 33(1977), pp. 337–347) include all those which are likely to arise in applications. Examples of conditional convergence of the series to step functions and to ramp functions are presented. Problems previously considered to be intractable to analysis are solved by analysis.

140 citations


Journal ArticleDOI
26 Aug 1977-Science
TL;DR: Application of the D'Arch Thompson method to hominid skull phylogeny has demonstrated three principal axes of evolutionary change anatomically homologous over a fossil sequence.
Abstract: In 1917, D'Arch Thompson suggested that one should study the change from one biological form to another by examining the unique mathematical object that maps between them in accord with biological homologies. Biorthogonal grids provide a particular coordinate system for visualizing such a map and lead to a quantitative syntax in which a change in shape is reduced to differential changes in size. Application of the method to hominid skull phylogeny has demonstrated three principal axes of evolutionary change anatomically homologous over a fossil sequence.

23 citations


Journal ArticleDOI
TL;DR: In this article, a biorthogonal set of expansion functions is introduced for the radial mode problem that occurs for drift waves and trapped particle modes in nonuniform plasmas.
Abstract: A biorthogonal set of expansion functions is introduced for the radial mode problem that occurs for drift waves and trapped particle modes in nonuniform plasmas. With a vector space representation of the eigenfunctions concise time dependent and time independent perturbation theory formulae are obtained for the system.

5 citations


Journal ArticleDOI
TL;DR: In this paper, a biorthogonal expansion in terms of the system, where are the zeros of the entire function and has bounded variation for some integer, for, and.
Abstract: We consider a biorthogonal expansion in terms of the system , where are the zeros of the entire function and has bounded variation for some integer , for , and . The function to be expanded has domain . We describe the sets of convergence (and divergence) of the series for the classes , , , and . The results indicate that the series have properties different from those of ordinary Fourier series; and the difference becomes more pronounced as increases.Bibliography: 16 titles.

3 citations


Journal ArticleDOI
TL;DR: By using Abel's integral equations, this article solved dual series equations involving Konhauser's biorthogonal polynomial set of the first kind by using Abel integral equations.
Abstract: By using Abel’s integral equations, we solve dual series equations involving Konhauser’s biorthogonal polynomial set of the first kind.

2 citations


Journal ArticleDOI
TL;DR: In this article, the connection between the Riesz means of expansions of in a trigonometric series and in a biorthogonal series in the eigenfunctions and associated functions of a non-selfadjoint differential operator of order is studied.
Abstract: For any function , the connection between the Riesz means of expansions of in a trigonometric series and in a biorthogonal series in the eigenfunctions and associated functions of a nonselfadjoint differential operator of order is studied.Bibliography: 6 titles.